NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2015, 6 (1), P. 146–153
STRONG SOLUTIONS AND THE INITIAL DATA SPACE FOR SOME NON-UNIFORMLY PARABOLIC EQUATIONS
M. A. Skryabin – ITMO University, Saint Petersburg, Russia; email@example.com
This paper is devoted to strong solutions of the first and second initial-boundary problems for non-uniformly parabolic equations. These equations are used in mechanics, glaciology, rheology, image processing as well as for nanosystem modeling. The initial data space for these problems was explicitly described as Orlicz—Sobolev spaces.
Keywords: non-uniformly parabolic equation, strong solution, initial data space, Orlicz—Sobolev space.